Lab 13 - Electrochemistry and the Nernst Equation

Goal and Overview

A voltmeter is used to study the relative reduction potential of various metals and the concentration dependence of voltage in concentration cells. The solubility of silver halides will be determined by measuring the voltage of a saturated solution against a standard solution of Ag⁺ ions. From the solubility, the values of

K_sp

for AgCl, AgBr, and AgI will be calculated.

Objectives and Science Skills

• •
  Understand and explain the chemistry, components, function, and operation of electrochemical and concentration cells.
• •
  Construct electrochemical cells and measure E⁰_cell for different pairs of metals and metal ion solutions; identify anode and cathode and explain what occurs at each (oxidation or reduction).
• •
  Construct concentration cells and measure E_cell values; use experimental values to calculate K_sp for slightly soluble silver halide salts.
• •
  Quantitatively and qualitatively compare experimental results with theoretical values.
• •
  Identify and discuss factors or effects that may contribute to the uncertainties in values determined from experimental data.

Suggested review and external reading

• •
  relevant reference information and/or textbook information on thermodynamics, electrochemistry, equilibrium, and free energy

Background

The primary measurement in electrochemistry is the voltage (V) of an electrochemical cell. The voltage describes the relative energies of electrons on different atoms and/or ions. The energy difference, or potential difference, between two electrons is measured in volts (joules/coulomb). The electrons may be on two ends of a wire, on two atoms, or on the cathode and anode of a battery having a potential difference. An oxidation-reduction or redox reaction is a chemical reaction in which one or more electrons from one molecule or atom are transferred to another. Thermodynamics can predict if electrons would prefer to be transferred from one species to another based on the free energy change of the system. For example, electrons are more stable on copper than zinc, so if a piece of zinc is placed in a copper ion solution, the electrons will spontaneously transfer from Zn to Cu²⁺, where they are more stable. It is possible for a redox reaction to occur in such a way that the electrons cannot jump directly from one particle to another. Instead, the electrons are forced to flow through an external electrical circuit. This type of device is called a voltaic cell. Consider the zinc-copper cell shown below. Zn atoms spontaneously give up 2 electrons and enter the solution as Zn²⁺ ions. The electrons flow through the external circuit into the Cu electrode. At the surface of the electrode, Cu²⁺ ions pick up the electrons and are reduced to Cu atoms. There is a 'push' on the electrons from the Zn side of the cell to the Cu side. A salt bridge keeps charges from accumulating on one side or the other, thus maintaining charge neutrality. If the external circuit is open so electrons cannot flow freely through it, electrons pile up on the left-hand side of the broken circuit and are depleted on the right-hand side, which results in the potential difference or cell potential (measured in volts). The cell voltage is proportional to ΔG, the change in Gibbs free energy. The ΔG of the reaction could be harnessed to do useful electrical work. The value of ΔG is given by this thermodynamic equation. ΔG° is the change in Gibbs free energy for the process when all the reactants and products are in their standard states. For gases, the standard state is the pure gas at 1 atm pressure; for ions in solution, 1 mol/L (1 M). The standard state of solids and liquid solvents are the pure solids or liquids. Q is the reaction quotient for the reaction. Q has the same form as the equilibrium constant, K, but the concentrations and/or gas pressures in Q are the instantaneous values in the non-equilibrium reaction vessel, rather than a set of values that characterize equilibrium. The relationship between cell voltage, E, and ΔG for the cell reaction is given by the following equation. The nF term is related to the coulombs of negative charge transferred in the balanced redox reaction. The number of moles of electrons transferred is given by n. F is Faraday's constant, which is the total charge (in coulombs) of a mole of electrons. A process will spontaneously occur if there is a decrease in free energy, G, or ΔG < 0. From Eq. 3,

ΔG = −nFE, or E = −ΔG/nF 

this implies spontaneity is associated with a positive E. If Eqs. 3

ΔG = −nFE, or E = −ΔG/nF 

and 4

F = 96,485

coulomb

mole e−

= 96,485

Joule

mole − volt

 

are used in Eq. 2,

ΔG = ΔG° + RT ln Q

 

the result is the Nernst equation. The Nernst equation includes a term that reflects the potential difference between products and reactants under standard conditions (E°) and a term to account for non-standard conditions

(RT / nF × ln Q). 

This simplifies for the special case of a cell at 25°C (and using

2.303 log₁₀ x = log_e x = ln x). 

E is the voltage measured for the cell. E° is the voltage measured when

Q = 1. 

The value 0.0591 is the same for all cells at 25°C. E° is also related to the electron energy differences of the oxidation and reduction reaction. E°_1/2(reduction) is the standard reduction half potential of the reduction reaction, and E°_1/2(oxidation) is the reduction half potential of the oxidation reaction. For a spontaneous reaction, the species with the most positive value of E°_1/2 will be reduced and the other species will be oxidized. If the concentrations of reactants and products are those characteristic of chemical equilibrium, then it is not possible to get any useful electrical work out of the cell. E equals zero. Setting

E = 0 

in Eq. 6

E = E° −

(0.0591 volts)

n

log₁₀ Q

 

results in the equation below. Here, K_eq is the equilibrium constant for the reaction as written. K_eq can be determined directly from a measured E° under standard conditions.

Procedure

Please use small volumes of solution to reduce the cost of buying chemicals and the problems with waste disposal. Dispose of all waste as instructed. Waste solutions must be segregated according to type. Read the labels on the waste bottles carefully. Clean up all spills. DO NOT THROW ELECTRODES AWAY. Please return them CLEAN. Please dispose of the used vials and salt bridges in the solid waste container in the back hood. Wash your hands thoroughly and carefully when done. If you do not dispose of waste correctly, you may lose points.

Part 1: Determinations of E° for Metals vs. Copper

For the redox reaction

A(s) + B²⁺ A²⁺ + B(s) 

the Nernst equation is shown below. The metal ion solutions are 0.10 M. Because the concentrations of both solutions are equal (0.10 M), Q will be 1, log Q will be 0, and the measured E will equal E°. The value of n is two because A loses 2 electrons and B gains two as written in the redox reaction. You are experimentally finding the relative 'push' on electrons from one species to another.

To create a voltaic cell:

To create the salt bridge:

Part 2: Dependence of E on Ion Concentrations

In part 1 you measured E° values. In part 2, you will read about how E depends on concentration of ions in a concentration cell. In a concentration cell, both electrodes are made of the same metal and the solutions in the cells are of the same ion as the electrodes. The difference between the cells lies in the metal ion concentration. In this case, the chemical reaction is given below. E° is zero for a concentration cell because the half reactions are identical in both directions. The Nernst equation becomes the following. The spontaneous direction for the reaction is from left to right when Ag⁺_conc (c₁) is greater than Ag⁺_dil (c₂).

• •
  In cell 1, ions accept electrons from the metal, plate out on the electrode, and lower the concentration of the ions.
• •
  In cell 2, atoms in the metal leave electrons behind and enter the solution, thus raising the ion concentration.
• •
  The reaction occurs in such a direction as to equalize the concentrations of the two solutions.

Your TA will tell you if you need to perform this part of the experiment. IF YOU DO NOT PERFORM PART 2, use the slope of the given Nernst plot for the

K_sp

determinations in part 3.

NOTE:

Depending on the lab schedule, part 2 might be omitted. Your TA will inform you in lab. If part 2 is not performed, use the plot that would be obtained ideally (theoretical) from plotting E vs. log([Ag⁺_dil]/[Ag⁺_conc]). Theoretical slope = –0.0591 V.

Part 3: Determination of K_sp of Very Insoluble Silver Halides

In this step you will determine the concentration of Ag⁺ ion in a saturated solution of silver halides (AgCl, AgBr, and AgI) by measuring the voltage of a concentration cell in which the silver halide solution is paired with 0.10 M Ag⁺. There are 0.20 M stock solutions of KCl, KBr, and KI. To measure K_sp for AgCl: Waste Disposal: Dispose of all waste as instructed. Clean up your work area. Wash your hands. Waste Disposal: Dispose of all waste as instructed. Clean up your work area. Wash your hands.

Results

Complete your lab summary or write a report (as instructed).

Abstract

Results

• Part 1. Data and Results table
  • E_measured for various metals relative to Cu (i.e. Cu__M₁),
  • E°(cell) predicted using metals other than copper
• Part 2. Data and Results Table if done
  • c₁(0.10 M), c₂, E_measured, and log(c₂/c₁)
  • graph E versus log (c₂/c₁), and determine the slope
• Part 3. Data and Results
  • E_measured, c_Ag⁺, K_sp for AgCl, AgBr, AgI, and ΔG°

Sample Calculations

• Part 1. Predicted E° for cells with metals vs. Cu
• Part 2. log(c₂/c₁) if done
• Part 3. [Ag⁺], K_sp(AgCl), ΔG°(AgCl solubility), K_sp(AgBr), ΔG°(AgBr solubility), K_sp(AgI), ΔG°(AgI solubility)

Discussion/Conclusions

• Part 1: Does E_measured agree with E_predicted for the various metals?
• Part 2: Does the slope agree with the slope predicted by the Nernst equation?
• Part 1 and 2:
  • Even though cell potentials are affected by both concentration differences and voltage differences between different metals, you were able to determine the dependence on each factor (RT / nF and E_1/2°). How were the individual dependencies separated out and determined individually?
• Part 3: How does part 3 depend on part 2?

Review

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